JournalszaaVol. 3, No. 2pp. 167–178

Some properties of a new kind of modulus of smoothness

  • Vilmos Totik

    University of Szeged, Hungary
Some properties of a new kind of modulus of smoothness cover
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Abstract

The modulus of smoothness

ω(f,δ)φ,p=sup0<h≤δ∥Δh,φ2∥Lp\omega (f, \delta)_{\varphi, p} = \mathrm {sup}_{0 < h ≤ \delta} \| \Delta^2_{h, \varphi} \|_{L^p}

has arisen during the investigation of positive operators of the Kantorovich type. Here we show that ωφ,p\omega_{\varphi, p} resembles the ordinary case φ=1\varphi = 1 and we give the characterization of those functions ff for which ω(f,δ)φ,p=O(δ2)\omega (f, \delta)_{\varphi, p} = O (\delta^2). The results obtained have applications to positive operators.

Cite this article

Vilmos Totik, Some properties of a new kind of modulus of smoothness. Z. Anal. Anwend. 3 (1984), no. 2, pp. 167–178

DOI 10.4171/ZAA/98